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User blog:Edwin Shade/A Formalist Approach to Numerical Symbolism
According to the Biblical interpretation of various numbers (see the last part of this webpage), there are various meanings assigned to some numbers, which is part of the symbology used in the book of Revelation and occasionally elsewhere in the Bible. Of course, one thing I’ve wondered about was if 2 is supposed to represent confirmation and 4 completeness, then what could the act of multiplying 2 by 2 possibly represent? In other words, how is a symbolic view of the number line compatible with a formalist view of mathematics? Well, it isn't - because this confusion rests upon the assumption these symbolic numbers could be arbitrarily multiplied or concatenated to derive numbers with similar but subtler meanings. For instance, 666 is the number of the beast, which I wondered about. Was 666 representative of the beast because it's factors, 2, 3, 3, and 37 had a negative meaning, or because 6 was concatenated 3 times, and since 6=imperfection and 3=emphasis it means 666 denotes extreme imperfection, or something very monstrous and flawed? Clearly the latter according to Occam's razor. So then, you might assume that concatenation would be the way to combine lesser symbolic numbers to achieve greater symbolic numbers. But then there is the 144,000 in Revelation, which is derived from 12,000 taken out of every tribe of Israel, or 12,000 multiplied by 12. 12 is a number used to denote order in the Bible, so clearly 144,000 is derived from a very orderly divine arrangement (122 or 144) multiplied by 1,000, which is a number denoting a very orderly Earthly arrangement (being a power of 10, a number of Earthly perfection). So 666 is derived from concatenation but 144,000 from multiplication - this I accept, though it makes deriving other symbolic numbers difficult, for how are you supposed to know when to concatenate and when to multiply? It now seems most reasonable to me to suppose that Biblical numbers of symbology are very contextual, and should not be imbued with a formalism they do not possess. The purpose of the Bible after all, is to make the sovereignty of God and the reasons people should serve Him clear along with comforting and consoling imperfect people, not to be a mathematics textbook (though of course God is after all the best mathematician in (and outside of) the universe). Thus, at this point the Biblical endowment of certain natural numbers with figurative meaning will be used a base from which I will devise my own symbolical system, whose focus is a formalistic approach to numerical symbology rather than the thoughts of the symbology itself (though that will of course be included). Firstly we shall establish what the known Biblical interpretations of numbers are: Now to establish a concatenative view of numerical symbolism would be easy but it would make things uncertain - for instance, is there a difference between 67 and 76? Also, the base you are using is important, and so concatenation is heavily bias towards a base 10 number system. A multiplicative view of numerical symbolism is what I’m after. We must create a system where each number may derived in a unique way and there is no ambiguity as to interpretation. As it turns out, the fundamental theorem of arithmetic provides the framework we need to make this work. Every number has a unique prime factorization or is itself a prime, therefore every number can be assigned a different meaning. These known Biblical numbers will be the starting base, or first level of numerical symbolism. Now these can be related to the prime numbers by the function f(n)=Pn, which will be the components for the second leve of symbolism. Note these levels are independent of each other, which resolves the disparity between multiplicative relations and symbolism. On the second base of symbolism will be the primes corresponding the first level of Biblical numbers, 1, 2, 3, 4, etc… For instance, the prime corresponding to divine perfection or completion would be f(7) or P7, the seventh prime, or 17. The prime of imperfection would be P6 or 13. Therefore, a slightly more abstruse but equally valid rewriting of 666 would be 371,293, 13 multiplied by itself five times. We are multiplying 13 by itself 5 times because 5 is P3, the prime correspondence of 3 for emphasis in the second level of numerical symbolism. For the number 12, the second-order symbolism would be P12, or 37, the prime corresponding to 12. As 37 is part of the prime factorization of 777, which is 3*7*37, it seems the meaning behind 777 would be 3 (the second order symbolism of 2 denoting affirmation or duality) multiplied by 7 (the second order symbolism of 4 denoting completeness of four fold symmetry) multiplied by 37 (which we established means order). So what is certain, has completeness or four fold symmetry, and order? The meaning of 777 is not totally clear, but it could be a reference to the establishment of God’s Kingdom on Earth. As the Earthly lands are often described as possessing four corners, (Ezekiel 7:2, Revelation 7:28), and the establishment of God’s purpose is sure and orderly, 777 seems like an appropriate number to assign to God’s Kingdom on Earth, in second-order symbolism. In first-order symbolism 777 would denote an emphasis (3 digits) on divine completion (7), but, by such a definition 777 could symbolize fulfillment of not just God’s purpose but Satan’s. So, by going up one level of symbolism we are able to deduce a more precise interpretation of the number 777, (though numbers in one level of symbolism do not always mean the same thing in higher symbolic levels, in this case it happened to work out that way). Of interest is that the second-order interpretation of 666 is unity 2 (P1), affirmation 3 (P2) multiplied by itself twice (P1 again), multiplied by order (37) - nothing here hints at a monstrous beast or evil; hence a lesson why we should not carry the meanings of lower order symbolism into the realm of higher-order symbolism and vice versa. As pertains to googology, large numbers can be derived by diagonalizing over the orders of symbolism themselves. So for instance, a tertiary interpretation of 7 would be PP7 or P17 or 59. But how about the seventh interpretation of 7? This would be PPPPPP7, or 167,449, a truly divine number, but also rather large. What if we took the 167,449th symbolism of 167,449? Then we are ascending into levels of numerical meaning no human mind may fully comprehend, but that are very real and extremely large (only at exponential level, yes, but these numbers would have millions of digits). These are prime numbers we will likely never be able to calculate with Earthly technology, but may nonetheless be known quite commonly in heaven (for I believe there are are quite a few mathematically inclined Cherubs and Seraphs there). To make an exhaustive list of all second-order (secondary), third-order (tertiary), fourth-order (quandary), symbolisms would not only be tedious but impossible. But I have laid the framework for further exploration clearly in this blog post, and this may very well be explored further, along with a better notation and possible adjustment as I develop this further. Category:Blog posts